The Double Tidal Bulge

If you look at any explanation of tides the force is indeed real. Try driving same for all points on the Earth. Try you will see a diagram that looks fast around a tight bend and tell me this analogy: take something round something like fig.1 which shows the you can’t feel a force pushing you to like a roll of sticky tape, put it on the tides represented as two bulges of the side. You are in the rotating desk and move it in small circles (not water – one directly under the Moon frame of reference hence the force rotating it, just moving the whole and another on the opposite side of can be felt. thing it in a circular manner). You will the Earth. Most people appreciate see that every point on the object that tides are caused by gravitational 3. In the discussion about what moves in a circle of equal radius and forces and so can understand the causes the two bulges of water you the same speed. moon-side bulge; however the must completely ignore the rotation second bulge is often a cause of of the Earth on its axis (the 24 hr Now let’s look at the gravitation pull confusion. This article attempts to daily rotation). Any talk of rotation experienced by objects on the Earth explain why there are two bulges. refers to the 27.3 day rotation of the due to the Moon. The magnitude and Earth and Moon about their common direction of this force will be different centre of mass. at different points on the Earth’s surface. The equation for the So let’s look at the forces acting at magnitude of gravitational force different points on the Earth’s between two objects is: surface. In fig 2, the blue arrows are the forces due to the gravitational fig 1: the double bulge of water attraction of the moon. The red

Before we look at this in detail, we arrows are the centrifugal force need to clarify a few points. experienced by bodies on the earth. (m1 and m2 is the mass of the two The size of the arrow approximates objects, and r is the distance 1. The Moon does not orbit around the magnitude of the force. The between them) the Earth. “What!” I hear you cry, “of scale is highly exaggerated. course it does – they taught me that This shows that the strength of the at school.” In reality, the moon and force is inversely proportional to the earth both orbit around each other, square of the distance between them or more precisely around their (i.e. if the distance doubles, the force common centre of mass which is reduced by a factor of four). happens to lie inside the Earth. Therefore the magnitude will be slightly greater on the side of the

2. There are two forces acting on the Earth nearest the Moon than on the Earth’s oceans and seas: gravity due fig 2: the red arrows representing the side of the Earth facing away from to the presence of the moon and a centrifugal force are the same at all the moon as it is further away. The centrifugal force due to the rotational points on the Earth. direction of the force is always motion of the Earth-Moon system. At Firstly you will notice that all the red towards the centre of the Moon. this point some scientists will argue arrows are exactly the same length. The resultant force that acts on the that centrifugal forces are fictitious. If This is because the 27.3 day rotation you are looking at the system from a water in our oceans (which we shall of the earth about the Earth-Moon call the tidal force) is a combination fixed point in space (an inertial or centre of mass causes every point non-accelerating frame of reference) of these two forces. If you add them on the earth to move in a circle of together you get the small green then this is correct. However, if you equal radius at equal speed. are in a rotating frame of reference, Therefore the centrifugal force is the

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You can probably see now why the bulges occur both on the side of the Earth facing the Moon and on the side of the Earth away from the Moon.

The explanation above takes into account just the Moon, although the sun also creates its own double fig 3: green arrows represent the bulge. When the Earth, Moon and resultant force Sun are in line (at full and new Moon), the position of the lunar and solar bulges coincides and the tides arrows shown in fig 3 (again, not to from the Earth (points marked Y), are higher than average. These are scale). then there is no force acting called spring tides. When the Earth, horizontally at the Earth’s surface (it Moon and Sun form a right-angle The force of gravity at the centre of is all either into or away from the (first and third quarter), the effect is the Earth balances the centrifugal Earth). Therefore there is no force to for them to partially cancel each force (i.e. is equal in magnitude but cause any movement of water other out and create what are known in exactly the opposite direction, across the Earth’s surface. However as neap tides. In fig 6 showing the therefore no net force) at points in between, there is going forces at neap tides, the black In fact the diagram below shows the to be some component of the force arrows represent the lunar tractive tidal forces and numerous points on which does act horizontally and this force and the red arrows show the the Earth’s surface. will cause a movement of water – an solar tractive force. obvious requirement for tides. These distribution of these horizontal components of the tidal force (known as the tractive force) is shown below.

fig 4: the resultant force at various points fig 6: at neap tides the lunar and solar on the Earth’s surface tractive forces are pushing the water in opposite directions diminishing the If a force is acting directly towards fig 5: the tractive force – the force flowing overall tide. the centre of the Earth (as at the horizontally across the Earth’s surface points marked X) or directly away